4. A set of points (finite or infinite) in the plane is called conver if for any two points P and Qin the set, the entire line segment with the endpoints at P and Q belongs to the set. The conver hull of a set 5 of points is the smallest convex set containing 5 in the plane. The conver-hull problem is the problem of constructing the convex hull for a given set S of n points. One of the solution to construct the convex-hull for a given set is to use the divide-and-conquer strategy. You can find such a solution from many Algorithm textbook or by googling it on WWW. Now, we consider the shortest path around problem defined as follows. There is a fenced area in the two-dimensional Euclidean plane in the shape of a convex polygon with vertices at points P₁(21, 3₁), P₂(22, y2),..., Pn(n, yn) (not necessarily in this order). There are two more points A(ZA, YA) and B(zB, YB), such that A < min{21, 22,...,n} and zB > max{1,2,...,n}. Design a reasonably efficient algorithm for computing the length of the shortest path between A and B. Note that the path cannot cross inside the fenced area but it can go along the fence. Please argue the correctness and time complexity of your algorithm.
4. A set of points (finite or infinite) in the plane is called conver if for any two points P and Qin the set, the entire line segment with the endpoints at P and Q belongs to the set. The conver hull of a set 5 of points is the smallest convex set containing 5 in the plane. The conver-hull problem is the problem of constructing the convex hull for a given set S of n points. One of the solution to construct the convex-hull for a given set is to use the divide-and-conquer strategy. You can find such a solution from many Algorithm textbook or by googling it on WWW. Now, we consider the shortest path around problem defined as follows. There is a fenced area in the two-dimensional Euclidean plane in the shape of a convex polygon with vertices at points P₁(21, 3₁), P₂(22, y2),..., Pn(n, yn) (not necessarily in this order). There are two more points A(ZA, YA) and B(zB, YB), such that A < min{21, 22,...,n} and zB > max{1,2,...,n}. Design a reasonably efficient algorithm for computing the length of the shortest path between A and B. Note that the path cannot cross inside the fenced area but it can go along the fence. Please argue the correctness and time complexity of your algorithm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. A set of points (finite or infinite) in the plane is called conver if for any two points P and
Qin the set, the entire line segment with the endpoints at P and Q belongs to the set.
The convex hull of a set S of points is the smallest convex set containing S in the plane.
The conver-hull problem is the problem of constructing the convex hull for a given set
S of n points. One of the solution to construct the convex-hull for a given set is to use the
divide-and-conquer strategy. You can find such a solution from many Algorithm textbook
or by googling it on WWW. Now, we consider the shortest path around problem
defined as follows. There is a fenced area in the two-dimensional Euclidean plane in the
shape of a convex polygon with vertices at points P₁(21, 31), P₂(22, 32),..., Pn (En, yn) (not
necessarily in this order). There are two more points A(ZA, YA) and B(TB, YB), such that
TA < min{1, 2,...,n} and zB > max{1,2,...,n). Design a reasonably efficient
algorithm for computing the length of the shortest path between A and B. Note that the
path cannot cross inside the fenced area but it can go along the fence. Please argue the
correctness and time complexity of your algorithm.
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